Question

suppose a life insurance company sells a $220,000 1 - year term life insurance policy to a 20 - year - old female for $120. according to the national vital statistics report, 58(21), the probability that the female survives the year is 0.999544. compute and interpret the expected value of this policy to the insurance company.
the expected value is $ 219.60
(round to the nearest cent as needed.)
which of the following interpretations of the expected value is correct? select the correct choice below and fill in the answer box to complete your choice
(round to the nearest cent as needed.)
a. the insurance company expects to make a profit of $ on every 20 - year - old female it insures for 1 year.
b. the insurance company expects to make a maximum profit of $ on every 20 - year - old female it insures for 1 year
c. the insurance company expects to make a minimum profit of $ on every 20 - year - old female it insures for 1 month.
d. the insurance company expects to make a profit of $ on every 20 - year - old female it insures for 1 month

Explanation:

Step1: Calculate the profit when the female survives

If the female survives, the insurance company's profit is the premium it charges. The premium is \(P_1 = 120\) dollars, and the probability of survival \(p_1=0.999544\)

Step2: Calculate the profit when the female does not survive

If the female does not survive, the insurance company has to pay out \(220000\) dollars. So its profit is \(P_2=120 - 220000=- 219880\) dollars. The probability of not - surviving \(p_2 = 1 - 0.999544=0.000456\)

Step3: Calculate the expected value \(E(X)\)

The formula for the expected value of a discrete random variable \(E(X)=\sum_{i}x_ip_i\). Here, \(E(X)=P_1p_1 + P_2p_2\)

$$
LATEXBLOCK0
$$

Answer:

A. The insurance company expects to make a profit of \(19.58\) on every 20 - year - old female it insures for 1 year.